From 9e236224f4c084ee4263ed2250bc6e674467fcdd Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Fri, 26 Apr 2024 16:22:47 +0000 Subject: [PATCH] build based on 292b71f --- .../previews/PR220/.documenter-siteinfo.json | 1 + .../previews/PR220/api/index.html | 45 + .../previews/PR220/assets/documenter.js | 1050 +++++++++++++++++ .../previews/PR220/assets/favicon.ico | Bin 0 -> 121769 bytes .../previews/PR220/assets/logo.jl | 674 +++++++++++ .../previews/PR220/assets/logo.svg | 20 + .../PR220/assets/themes/documenter-dark.css | 7 + .../PR220/assets/themes/documenter-light.css | 9 + .../previews/PR220/assets/themeswap.js | 84 ++ .../previews/PR220/assets/warner.js | 52 + .../previews/PR220/backends/index.html | 12 + .../previews/PR220/design/index.html | 7 + .../previews/PR220/extensions/index.html | 7 + .../previews/PR220/index.html | 23 + .../previews/PR220/objects.inv | Bin 0 -> 1872 bytes .../previews/PR220/overloads/index.html | 55 + .../previews/PR220/overview/index.html | 7 + .../previews/PR220/search_index.js | 3 + .../previews/PR220/siteinfo.js | 1 + .../previews/PR220/tutorial/index.html | 28 + 20 files changed, 2085 insertions(+) create mode 100644 DifferentiationInterface/previews/PR220/.documenter-siteinfo.json create mode 100644 DifferentiationInterface/previews/PR220/api/index.html create mode 100644 DifferentiationInterface/previews/PR220/assets/documenter.js create mode 100644 DifferentiationInterface/previews/PR220/assets/favicon.ico create mode 100644 DifferentiationInterface/previews/PR220/assets/logo.jl create mode 100644 DifferentiationInterface/previews/PR220/assets/logo.svg create mode 100644 DifferentiationInterface/previews/PR220/assets/themes/documenter-dark.css create mode 100644 DifferentiationInterface/previews/PR220/assets/themes/documenter-light.css create mode 100644 DifferentiationInterface/previews/PR220/assets/themeswap.js create mode 100644 DifferentiationInterface/previews/PR220/assets/warner.js create mode 100644 DifferentiationInterface/previews/PR220/backends/index.html create mode 100644 DifferentiationInterface/previews/PR220/design/index.html create mode 100644 DifferentiationInterface/previews/PR220/extensions/index.html create mode 100644 DifferentiationInterface/previews/PR220/index.html create mode 100644 DifferentiationInterface/previews/PR220/objects.inv create mode 100644 DifferentiationInterface/previews/PR220/overloads/index.html create mode 100644 DifferentiationInterface/previews/PR220/overview/index.html create mode 100644 DifferentiationInterface/previews/PR220/search_index.js create mode 100644 DifferentiationInterface/previews/PR220/siteinfo.js create mode 100644 DifferentiationInterface/previews/PR220/tutorial/index.html diff --git a/DifferentiationInterface/previews/PR220/.documenter-siteinfo.json b/DifferentiationInterface/previews/PR220/.documenter-siteinfo.json new file mode 100644 index 000000000..5aeb39263 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-26T16:22:41","documenter_version":"1.4.0"}} \ No newline at end of file diff --git a/DifferentiationInterface/previews/PR220/api/index.html b/DifferentiationInterface/previews/PR220/api/index.html new file mode 100644 index 000000000..d7bc51256 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/api/index.html @@ -0,0 +1,45 @@ + +API reference · DifferentiationInterface.jl
GitHub

API reference

DifferentiationInterface — Module
DifferentiationInterface

An interface to various automatic differentiation backends in Julia.

Exports

source

Derivative

Gradient

Jacobian

DifferentiationInterface.prepare_jacobian — Function
prepare_jacobian(f,     backend, x) -> extras
+prepare_jacobian(f!, y, backend, x) -> extras

Create an extras object subtyping JacobianExtras that can be given to Jacobian operators.

Beware that in the two-argument case, y is mutated by f! during preparation.

source

Second order

DifferentiationInterface.SecondOrder — Type
SecondOrder

Combination of two backends for second-order differentiation.

Constructor

SecondOrder(outer, inner)

Fields

  • outer::ADTypes.AbstractADType: backend for the outer differentiation

  • inner::ADTypes.AbstractADType: backend for the inner differentiation

source

Primitives

DifferentiationInterface.prepare_pushforward — Function
prepare_pushforward(f,     backend, x, dx) -> extras
+prepare_pushforward(f!, y, backend, x, dx) -> extras

Create an extras object subtyping PushforwardExtras that can be given to pushforward operators.

Beware that in the two-argument case, y is mutated by f! during preparation.

source
DifferentiationInterface.prepare_pullback — Function
prepare_pullback(f,     backend, x, dy) -> extras
+prepare_pullback(f!, y, backend, x, dy) -> extras

Create an extras object subtyping PullbackExtras that can be given to pullback operators.

Beware that in the two-argument case, y is mutated by f! during preparation.

source

Backend queries

DifferentiationInterface.check_hessian — Function
check_hessian(backend)

Check whether backend supports second order differentiation by trying to compute a hessian.

Warning

Might take a while due to compilation time.

source

Translation

DifferentiationInterface.DifferentiateWith — Type
DifferentiateWith

Callable function wrapper that enforces differentiation with a specified (inner) backend.

This works by defining new rules overriding the behavior of the outer backend that would normally be used.

Warning

This is an experimental functionality, whose API cannot yet be considered stable. At the moment, it only supports one-argument functions, and rules are only defined for ChainRules.jl-compatible outer backends.

Fields

  • f: the function in question
  • backend::AbstractADType: the inner backend to use for differentiation

Constructor

DifferentiateWith(f, backend)

Example

using DifferentiationInterface
+import ForwardDiff, Zygote
+
+function f(x)
+    a = Vector{eltype(x)}(undef, 1)
+    a[1] = sum(x)  # mutation that breaks Zygote
+    return a[1]
+end
+
+dw = DifferentiateWith(f, AutoForwardDiff());
+
+gradient(dw, AutoZygote(), [2.0])  # calls ForwardDiff instead
+
+# output
+
+1-element Vector{Float64}:
+ 1.0
source

Internals

This is not part of the public API.

DifferentiationInterface.CompressedMatrix — Type
CompressedMatrix{dir}

Compressed representation B of a sparse matrix A ∈ ℝ^{m×n} obtained by summing some of its columns (if dir == :col) or rows (if dir == :row), grouped by color.

Fields

  • sparsity::AbstractMatrix{Bool}: boolean sparsity pattern of the matrix A
  • colors::Vector{Int}: vector such that
    • if dir ==:col, thencolors[j] ∈ 1:cis the color of columnj`
    • if dir ==:row, thencolors[i] ∈ 1:cis the color of rowi`
  • groups::Vector{Vector{Int}}: vector of length c such that
    • if dir == :col, then groups[k] is the vector of column indices assigned to the same color k ∈ 1:c
    • if dir == :row, then groups[k] is the vector of row indices assigned to the same color k ∈ 1:c
  • aggregates::AbstractMatrix: matrix B such that
    • if dir == :col, then size(B) = (m, c) and B[:, c] = sum(A[:, k] for k in groups[c])
    • if dir == :row, then size(B) = (c, n) and B[c, :] = sum(A[k, :] for k in groups[c])
source
DifferentiationInterface.SymbolicsSparsityDetector — Type
SymbolicsSparsityDetector <: ADTypes.AbstractSparsityDetector

Sparsity detection algorithm based on the Symbolics.jl tracing system.

Compatible with the ADTypes.jl sparsity detection framework.

Danger

This functionality is implemented in an extension, and requires Symbolics.jl to be loaded.

See also

  • ADTypes.jacobian_sparsity
  • ADTypes.hessian_sparsity

Reference

Sparsity Programming: Automated Sparsity-Aware Optimizations in Differentiable Programming, Gowda et al. (2019)

source
ADTypes.mode — Method
mode(backend::SecondOrder)

Return the outer mode of the second-order backend.

source
DifferentiationInterface.basis — Method
basis(backend, a::AbstractArray, i::CartesianIndex)

Construct the i-th stardard basis array in the vector space of a with element type eltype(a).

Note

If an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.

source
DifferentiationInterface.pick_chunksize — Method
pick_chunksize(input_length)

Pick a reasonable chunk size for chunked derivative evaluation with an input of length input_length.

The result cannot be larger than DEFAULT_CHUNKSIZE=8.

source
diff --git a/DifferentiationInterface/previews/PR220/assets/documenter.js b/DifferentiationInterface/previews/PR220/assets/documenter.js new file mode 100644 index 000000000..c6562b558 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/DifferentiationInterface/previews/PR220/assets/favicon.ico b/DifferentiationInterface/previews/PR220/assets/favicon.ico new file mode 100644 index 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/DifferentiationInterface/previews/PR220/assets/themeswap.js b/DifferentiationInterface/previews/PR220/assets/themeswap.js new file mode 100644 index 000000000..9f5eebe6a --- /dev/null +++ b/DifferentiationInterface/previews/PR220/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/DifferentiationInterface/previews/PR220/assets/warner.js b/DifferentiationInterface/previews/PR220/assets/warner.js new file mode 100644 index 000000000..3f6f5d008 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/DifferentiationInterface/previews/PR220/backends/index.html b/DifferentiationInterface/previews/PR220/backends/index.html new file mode 100644 index 000000000..d30edb3e1 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/backends/index.html @@ -0,0 +1,12 @@ + +Backends · DifferentiationInterface.jl
GitHub

Backends

Types

We support all dense backend choices from ADTypes.jl, as well as their sparse wrapper AutoSparse.

For sparse backends, only the Jacobian and Hessian operators are implemented differently, the other operators behave the same as for the corresponding dense backend.

BackendAvailabilityTwo-argument functionsHessian supportExample
Diffractor (forward/reverse)✅❌❌AutoDiffractor()
Enzyme (forward)✅✅❌AutoEnzyme(; mode=Enzyme.Forward)
Enzyme (reverse)✅✅❌AutoEnzyme(; mode=Enzyme.Reverse)
FastDifferentiation (symbolic)✅✅✅AutoFastDifferentiation()
FiniteDiff (forward)✅✅✅AutoFiniteDiff()
FiniteDifferences (forward)✅❌✅AutoFiniteDifferences(; fdm=FiniteDifferences.central_fdm(3, 1))
ForwardDiff (forward)✅✅✅AutoForwardDiff()
PolyesterForwardDiff (forward)✅✅✅AutoPolyesterForwardDiff(; chunksize=1)
ReverseDiff (reverse)✅✅✅AutoReverseDiff()
Tapir (reverse)✅✅❌AutoTapir()
Tracker (reverse)✅❌❌AutoTracker()
Zygote (reverse)✅❌✅AutoZygote()
+

Availability

You can use check_available to verify whether a given backend is loaded.

Support for two-argument functions

All backends are compatible with one-argument functions f(x) = y. Only some are compatible with two-argument functions f!(y, x) = nothing. You can check this compatibility using check_twoarg.

Hessian support

Only some backends are able to compute Hessians. You can use check_hessian to check this feature.

API reference

Warning

The following documentation has been re-exported from ADTypes.jl. Refer to the ADTypes documentation for more information.

ADTypes.ADTypes — Module
ADTypes.jl

ADTypes.jl is a multi-valued logic system to choose an automatic differentiation (AD) package and specify its parameters.

source
ADTypes.AutoEnzyme — Type
AutoEnzyme{M}

Chooses Enzyme.jl.

Fields

  • mode::M: can be either
    • an object subtyping EnzymeCore.Mode (like EnzymeCore.Forward or EnzymeCore.Reverse) if a specific mode is required
    • nothing to choose the best mode automatically

Constructors

AutoEnzyme(; mode=nothing)
source
ADTypes.AutoFiniteDiff — Type
AutoFiniteDiff{T1,T2,T3}

Chooses FiniteDiff.jl.

Fields

  • fdtype::T1: finite difference type
  • fdjtype::T2: finite difference type for the Jacobian
  • fdhtype::T3: finite difference type for the Hessian

Constructor

AutoFiniteDiff(; fdtype=Val(:forward), fdjtype=fdtype, fdhtype=Val(:hcentral))
source
ADTypes.AutoForwardDiff — Type
AutoForwardDiff{chunksize,T}

Chooses ForwardDiff.jl.

Type parameters

  • chunksize: the preferred chunk size to evaluate several derivatives at once

Fields

  • tag::T: a custom tag to handle nested differentiation calls (usually not necessary)

Constructors

AutoForwardDiff(; chunksize=nothing, tag=nothing)
source
ADTypes.AutoSparse — Type
AutoSparse{D,S,C}

Wraps an ADTypes.jl object to deal with sparse Jacobians and Hessians.

Fields

Constructors

AutoSparse(
+    dense_ad;
+    sparsity_detector=ADTypes.NoSparsityDetector(),
+    coloring_algorithm=ADTypes.NoColoringAlgorithm()
+)
source
diff --git a/DifferentiationInterface/previews/PR220/design/index.html b/DifferentiationInterface/previews/PR220/design/index.html new file mode 100644 index 000000000..0362ca68d --- /dev/null +++ b/DifferentiationInterface/previews/PR220/design/index.html @@ -0,0 +1,7 @@ + +Package design · DifferentiationInterface.jl
GitHub

Package design

Backend requirements

To be usable with DifferentiationInterface.jl, an AD backend needs an object subtyping ADTypes.AbstractADType. In addition, some operators must be defined:

backend subtypepushforward necessarypullback necessary
ADTypes.ForwardModeyesno
ADTypes.ReverseModenoyes
ADTypes.SymbolicModeyesyes

Every backend we support corresponds to a package extension of DifferentiationInterface.jl (located in the ext subfolder). Advanced users are welcome to code more backends and submit pull requests!

diff --git a/DifferentiationInterface/previews/PR220/extensions/index.html b/DifferentiationInterface/previews/PR220/extensions/index.html new file mode 100644 index 000000000..26999182b --- /dev/null +++ b/DifferentiationInterface/previews/PR220/extensions/index.html @@ -0,0 +1,7 @@ + +Package extensions · DifferentiationInterface.jl
GitHub

Package extensions

Package extension content is not part of the public API. If any docstrings are present in an extension, they will appear below.

diff --git a/DifferentiationInterface/previews/PR220/index.html b/DifferentiationInterface/previews/PR220/index.html new file mode 100644 index 000000000..2da24ebb0 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/index.html @@ -0,0 +1,23 @@ + +Home · DifferentiationInterface.jl
GitHub

DifferentiationInterface

Build Status Coverage Code Style: Blue

PackageDocs
DifferentiationInterfaceStable Dev
DifferentiationInterfaceTestStable Dev

An interface to various automatic differentiation (AD) backends in Julia.

Goal

This package provides a backend-agnostic syntax to differentiate functions of the following types:

  • one-argument functions (allocating): f(x) = y
  • two-argument functions (mutating): f!(y, x) = nothing

Features

  • First- and second-order operators
  • In-place and out-of-place differentiation
  • Preparation mechanism (e.g. to create a config or tape)
  • Thorough validation on standard inputs and outputs (numbers, vectors, matrices)
  • Testing and benchmarking utilities accessible to users with DifferentiationInterfaceTest

Compatibility

We support all of the backends defined by ADTypes.jl v1.0:

Installation

To install the stable version of the package, run the following code in a Julia REPL:

julia> using Pkg
+
+julia> Pkg.add("DifferentiationInterface")

To install the development version, run this instead:

julia> using Pkg
+
+julia> Pkg.add(
+        url="https://github.com/gdalle/DifferentiationInterface.jl",
+        subdir="DifferentiationInterface"
+    )

Example

julia> import ADTypes, ForwardDiff
+
+julia> using DifferentiationInterface
+
+julia> backend = ADTypes.AutoForwardDiff();
+
+julia> f(x) = sum(abs2, x);
+
+julia> value_and_gradient(f, backend, [1., 2., 3.])
+(14.0, [2.0, 4.0, 6.0])
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GitHub

Table of overloads

As described in the overview, DifferentiationInterface provides multiple high-level operators like jacobian, each with several variants:

  • out-of-place or in-place return values
  • with or without primal output value
  • support for one-argument functions y = f(x) or two-argument functions f!(y, x)

To support a new backend, it is only required to define either a pushforward or a pullback function, since DifferentiationInterface provides default implementations of all operators using just these two primitives. However, backends sometimes provide their own implementations of operators, which can be more performant. When available, DifferentiationInterface always calls these backend-specific implementations, which we call "overloads".

The following tables summarize all implemented overloads for each backend. Each cell can have three values:

  • ❌: the operator is not overloaded because the backend does not support it
  • ✅: the operator is overloaded
  • NA: the operator does not exist
Tip

Check marks (✅) are clickable and link to the source code.

Diffractor (forward/reverse)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient❌❌❌❌
jacobian❌❌❌❌
hessian❌❌NANA
hvp❌❌NANA
pullback❌❌❌❌
pushforward✅❌✅❌
+

Two-argument functions f!(y, x)

+

Backend doesn't support mutating functions.

+

Enzyme (forward)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian✅✅✅✅
hessian❌❌NANA
hvp❌❌NANA
pullback❌❌❌❌
pushforward✅✅✅✅
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
jacobian❌❌❌❌
pullback❌❌❌❌
pushforward❌❌✅❌
+

Enzyme (reverse)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian❌❌❌❌
hessian❌❌NANA
hvp❌❌NANA
pullback✅✅✅✅
pushforward❌❌❌❌
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
jacobian❌❌❌❌
pullback❌❌✅❌
pushforward❌❌❌❌
+

FastDifferentiation (symbolic)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
gradient✅✅✅✅
jacobian✅✅✅✅
hessian✅✅NANA
hvp✅✅NANA
pullback✅✅✅✅
pushforward✅✅✅✅
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
jacobian✅✅✅✅
pullback✅✅✅✅
pushforward✅✅✅✅
+

FiniteDiff (forward)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
gradient✅✅✅✅
jacobian✅✅✅✅
hessian✅✅NANA
hvp❌❌NANA
pullback❌❌❌❌
pushforward✅❌✅❌
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
jacobian✅✅✅✅
pullback❌❌❌❌
pushforward❌❌✅❌
+

FiniteDifferences (forward)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian✅✅✅✅
hessian❌❌NANA
hvp❌❌NANA
pullback✅❌✅❌
pushforward✅❌✅❌
+

Two-argument functions f!(y, x)

+

Backend doesn't support mutating functions.

+

ForwardDiff (forward)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian✅✅✅✅
hessian✅✅NANA
hvp❌❌NANA
pullback❌❌❌❌
pushforward❌❌✅❌
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
jacobian✅✅✅✅
pullback❌❌❌❌
pushforward❌❌✅❌
+

PolyesterForwardDiff (forward)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
gradient✅✅✅✅
jacobian✅✅✅✅
hessian✅✅NANA
hvp❌❌NANA
pullback❌❌❌❌
pushforward✅✅✅✅
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative✅✅✅✅
jacobian✅✅✅✅
pullback❌❌❌❌
pushforward✅✅✅✅
+

ReverseDiff (reverse)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian✅✅✅✅
hessian✅✅NANA
hvp❌❌NANA
pullback❌❌✅✅
pushforward❌❌❌❌
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
jacobian✅✅✅✅
pullback✅✅✅✅
pushforward❌❌❌❌
+

Tapir (reverse)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient❌❌❌❌
jacobian❌❌❌❌
hessian❌❌NANA
hvp❌❌NANA
pullback✅✅✅✅
pushforward❌❌❌❌
+

Two-argument functions f!(y, x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
jacobian❌❌❌❌
pullback❌❌✅❌
pushforward❌❌❌❌
+

Tracker (reverse)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian❌❌❌❌
hessian❌❌NANA
hvp❌❌NANA
pullback❌❌✅❌
pushforward❌❌❌❌
+

Two-argument functions f!(y, x)

+

Backend doesn't support mutating functions.

+

Zygote (reverse)

One-argument functions y = f(x)

+
Operatoropop!value_and_opvalue_and_op!
derivative❌❌❌❌
gradient✅✅✅✅
jacobian✅✅✅✅
hessian✅✅NANA
hvp❌❌NANA
pullback❌❌✅❌
pushforward❌❌❌❌
+

Two-argument functions f!(y, x)

+

Backend doesn't support mutating functions.

+
diff --git a/DifferentiationInterface/previews/PR220/overview/index.html b/DifferentiationInterface/previews/PR220/overview/index.html new file mode 100644 index 000000000..a3f9755c3 --- /dev/null +++ b/DifferentiationInterface/previews/PR220/overview/index.html @@ -0,0 +1,7 @@ + +Overview · DifferentiationInterface.jl
GitHub

Overview

Operators

Depending on the type of input and output, differentiation operators can have various names.

We provide the following high-level operators:

operatororderinput xoutput yresult typeresult shape
derivative1NumberNumber or AbstractArraysame as ysize(y)
second_derivative2NumberNumber or AbstractArraysame as ysize(y)
gradient1AbstractArrayNumbersame as xsize(x)
hvp2AbstractArrayNumbersame as xsize(x)
hessian2AbstractArrayNumberAbstractMatrix(length(x), length(x))
jacobian1AbstractArrayAbstractArrayAbstractMatrix(length(y), length(x))

They can all be derived from two low-level operators:

operatororderinput xoutput yresult typeresult shape
pushforward (or JVP)1AnyAnysame as ysize(y)
pullback (or VJP)1AnyAnysame as xsize(x)

Luckily, most backends have custom implementations, which we reuse if possible instead of relying on fallbacks.

Tip

See the book The Elements of Differentiable Programming for details on these concepts.

Variants

Several variants of each operator are defined:

out-of-placein-placeout-of-place + primalin-place + primal
derivativederivative!value_and_derivativevalue_and_derivative!
second_derivativesecond_derivative!NANA
gradientgradient!value_and_gradientvalue_and_gradient!
hvphvp!NANA
hessianhessian!NANA
jacobianjacobian!value_and_jacobianvalue_and_jacobian!
pushforwardpushforward!value_and_pushforwardvalue_and_pushforward!
pullbackpullback!value_and_pullbackvalue_and_pullback!

Mutation and signatures

In order to ensure symmetry between one-argument functions f(x) = y and two-argument functions f!(y, x) = nothing, we define the same operators for both cases. However they have different signatures:

signatureout-of-placein-place
f(x)operator(f, backend, x, ...)operator!(f, result, backend, x, ...)
f!(y, x)operator(f!, y, backend, x, ...)operator!(f!, y, result, backend, x, ...)
Warning

Our mutation convention is that all positional arguments between f/f! and backend are mutated (the extras as well, see below). This convention holds regardless of the bang ! in the operator name, because we assume that a user passing a two-argument function f!(y, x) anticipates mutation anyway.

Still, better be careful with two-argument functions, because every variant of the operator will mutate y... even if it does not have a ! in its name (see the bottom left cell in the table).

Preparation

In many cases, AD can be accelerated if the function has been run at least once (e.g. to create a config or record a tape) and if some cache objects are provided. This is a backend-specific procedure, but we expose a common syntax to achieve it.

operatorpreparation function
derivativeprepare_derivative
gradientprepare_gradient
jacobianprepare_jacobian
second_derivativeprepare_second_derivative
hessianprepare_hessian
pushforwardprepare_pushforward
pullbackprepare_pullback
hvpprepare_hvp

Unsurprisingly, preparation syntax depends on the number of arguments:

signaturepreparation signature
f(x)prepare_operator(f, backend, x, ...)
f!(y, x)prepare_operator(f!, y, backend, x, ...)

The preparation prepare_operator(f, backend, x) will create an object called extras containing the necessary information to speed up operator and its variants. This information is specific to backend and f, as well as the type and size of the input x and the control flow within the function, but it should work with different values of x.

You can then call e.g. operator(backend, f, x2, extras), which should be faster than operator(f, backend, x2). This is especially worth it if you plan to call operator several times in similar settings: you can think of it as a warm up.

Warning

The extras object is nearly always mutated when given to an operator, even when said operator does not have a bang ! in its name.

Second order

We offer two ways to perform second-order differentiation (for second_derivative, hvp and hessian):

  • pick a single backend to do all the work
  • combine an "outer" and "inner" backend within the SecondOrder struct: the inner backend will be called first, and the outer backend will differentiate the generated code
Warning

There are many possible backend combinations, a lot of which will fail. At the moment, trial and error is your best friend. Usually, the most efficient approach for Hessians is forward-over-reverse, i.e. a forward-mode outer backend and a reverse-mode inner backend.

Experimental

Danger

Everything in this section is still experimental, use it at your own risk.

Sparsity

ADTypes.jl provides AutoSparse to accelerate the computation of sparse Jacobians and Hessians:

  • for sparse Jacobians, wrap AutoSparse around a first-order backend.
  • for sparse Hessians, wrap AutoSparse around a SecondOrder backend.

Split reverse mode

Some reverse mode AD backends expose a "split" option, which runs only the forward sweep, and encapsulates the reverse sweep in a closure. We make this available for all backends with the following operators:

out-of-placein-place
value_and_pullback_splitvalue_and_pullback!_split

Translation

The wrapper DifferentiateWith allows you to take a function and specify that it should be differentiated with the backend of your choice. In other words, when you try to differentiate dw = DifferentiateWith(f, backend1) with backend2, then backend1 steps in and backend2 does nothing. At the moment it only works when backend2 supports ChainRules.jl.

Going further

Non-standard types

The package is thoroughly tested with inputs and outputs of the following types: Float64, Vector{Float64} and Matrix{Float64}. We also expect it to work on most kinds of Number and AbstractArray variables. Beyond that, you are in uncharted territory. We voluntarily keep the type annotations minimal, so that passing more complex objects or custom structs might work with some backends, but we make no guarantees about that.

Multiple inputs/outputs

Restricting the API to one input and one output has many coding advantages, but it is not very flexible. If you need more than that, use ComponentArrays.jl to wrap several objects inside a single ComponentVector.

Batched evaluation

This is not supported at the moment, but we plan to allow several pushforward / pullback seeds at once (similar to the chunking in ForwardDiff.jl or the batches in Enzyme.jl).

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reference","text":"check_available\ncheck_twoarg\ncheck_hessian","category":"page"},{"location":"api/#DifferentiationInterface.check_available","page":"API reference","title":"DifferentiationInterface.check_available","text":"check_available(backend)\n\nCheck whether backend is available (i.e. whether the extension is loaded).\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.check_twoarg","page":"API reference","title":"DifferentiationInterface.check_twoarg","text":"check_twoarg(backend)\n\nCheck whether backend supports differentiation of two-argument functions.\n\n\n\n\n\n","category":"function"},{"location":"api/#DifferentiationInterface.check_hessian","page":"API reference","title":"DifferentiationInterface.check_hessian","text":"check_hessian(backend)\n\nCheck whether backend supports second order differentiation by trying to compute a hessian.\n\nwarning: Warning\nMight take a while due to compilation time.\n\n\n\n\n\n","category":"function"},{"location":"api/#Translation","page":"API reference","title":"Translation","text":"","category":"section"},{"location":"api/","page":"API reference","title":"API reference","text":"DifferentiateWith","category":"page"},{"location":"api/#DifferentiationInterface.DifferentiateWith","page":"API reference","title":"DifferentiationInterface.DifferentiateWith","text":"DifferentiateWith\n\nCallable function wrapper that enforces differentiation with a specified (inner) backend.\n\nThis works by defining new rules overriding the behavior of the outer backend that would normally be used.\n\nwarning: Warning\nThis is an experimental functionality, whose API cannot yet be considered stable. At the moment, it only supports one-argument functions, and rules are only defined for ChainRules.jl-compatible outer backends.\n\nFields\n\nf: the function in question\nbackend::AbstractADType: the inner backend to use for differentiation\n\nConstructor\n\nDifferentiateWith(f, backend)\n\nExample\n\nusing DifferentiationInterface\nimport ForwardDiff, Zygote\n\nfunction f(x)\n a = Vector{eltype(x)}(undef, 1)\n a[1] = sum(x) # mutation that breaks Zygote\n return a[1]\nend\n\ndw = DifferentiateWith(f, AutoForwardDiff());\n\ngradient(dw, AutoZygote(), [2.0]) # calls ForwardDiff instead\n\n# output\n\n1-element Vector{Float64}:\n 1.0\n\n\n\n\n\n","category":"type"},{"location":"api/#Internals","page":"API reference","title":"Internals","text":"","category":"section"},{"location":"api/","page":"API reference","title":"API reference","text":"This is not part of the public API.","category":"page"},{"location":"api/","page":"API reference","title":"API reference","text":"Modules = [DifferentiationInterface]\nPublic = false","category":"page"},{"location":"api/#DifferentiationInterface.AdjacencyGraph","page":"API reference","title":"DifferentiationInterface.AdjacencyGraph","text":"AdjacencyGraph\n\nRepresent a graph between the columns of a symmetric n × n matrix A with nonzero diagonal elements.\n\nThis graph is defined as G = (C, E) where C = 1:n is the set of columns and (i, j) ∈ E whenever A[i, j] is nonzero for some j ∈ 1:m, j ≠ i.\n\nFields\n\nA::AbstractMatrix\n\nReference\n\nWhat Color Is Your Jacobian? Graph Coloring for Computing Derivatives, Gebremedhin et al. (2005)\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.BipartiteGraph","page":"API reference","title":"DifferentiationInterface.BipartiteGraph","text":"BipartiteGraph\n\nRepresent a bipartite graph between the rows and the columns of a non-symmetric m × n matrix A.\n\nThis graph is defined as G = (R, C, E) where R = 1:m is the set of row indices, C = 1:n is the set of column indices and (i, j) ∈ E whenever A[i, j] is nonzero.\n\nFields\n\nA::AbstractMatrix\n\nReference\n\nWhat Color Is Your Jacobian? Graph Coloring for Computing Derivatives, Gebremedhin et al. (2005)\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.CompressedMatrix","page":"API reference","title":"DifferentiationInterface.CompressedMatrix","text":"CompressedMatrix{dir}\n\nCompressed representation B of a sparse matrix A ∈ ℝ^{m×n} obtained by summing some of its columns (if dir == :col) or rows (if dir == :row), grouped by color.\n\nFields\n\nsparsity::AbstractMatrix{Bool}: boolean sparsity pattern of the matrix A\ncolors::Vector{Int}: vector such that\nif dir ==:col, thencolors[j] ∈ 1:cis the color of columnj`\nif dir ==:row, thencolors[i] ∈ 1:cis the color of rowi`\ngroups::Vector{Vector{Int}}: vector of length c such that\nif dir == :col, then groups[k] is the vector of column indices assigned to the same color k ∈ 1:c\nif dir == :row, then groups[k] is the vector of row indices assigned to the same color k ∈ 1:c\naggregates::AbstractMatrix: matrix B such that\nif dir == :col, then size(B) = (m, c) and B[:, c] = sum(A[:, k] for k in groups[c])\nif dir == :row, then size(B) = (c, n) and B[c, :] = sum(A[k, :] for k in groups[c])\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.CompressedMatrix-Union{Tuple{dir}, NTuple{4, Any}} where dir","page":"API reference","title":"DifferentiationInterface.CompressedMatrix","text":"CompressedMatrix{dir}(sparsity, groups, aggregates)\n\nConstructor for CompressedMatrix.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.DerivativeExtras","page":"API reference","title":"DifferentiationInterface.DerivativeExtras","text":"DerivativeExtras\n\nAbstract type for additional information needed by derivative operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ForwardOverForward","page":"API reference","title":"DifferentiationInterface.ForwardOverForward","text":"ForwardOverForward\n\nTraits identifying second-order backends that compute HVPs in forward over forward mode (inefficient).\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ForwardOverReverse","page":"API reference","title":"DifferentiationInterface.ForwardOverReverse","text":"ForwardOverReverse\n\nTraits identifying second-order backends that compute HVPs in forward over reverse mode.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.GradientExtras","page":"API reference","title":"DifferentiationInterface.GradientExtras","text":"GradientExtras\n\nAbstract type for additional information needed by gradient operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.GreedyColoringAlgorithm","page":"API reference","title":"DifferentiationInterface.GreedyColoringAlgorithm","text":"GreedyColoringAlgorithm <: ADTypes.AbstractColoringAlgorithm\n\nMatrix coloring algorithm for sparse Jacobians and Hessians.\n\nCompatible with the ADTypes.jl coloring framework.\n\nSee also\n\nADTypes.column_coloring\nADTypes.row_coloring\nADTypes.symmetric_coloring\n\nReference\n\nWhat Color Is Your Jacobian? Graph Coloring for Computing Derivatives, Gebremedhin et al. (2005)\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.HVPExtras","page":"API reference","title":"DifferentiationInterface.HVPExtras","text":"HVPExtras\n\nAbstract type for additional information needed by Hessian-vector product operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.HessianExtras","page":"API reference","title":"DifferentiationInterface.HessianExtras","text":"HessianExtras\n\nAbstract type for additional information needed by Hessian operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.JacobianExtras","page":"API reference","title":"DifferentiationInterface.JacobianExtras","text":"JacobianExtras\n\nAbstract type for additional information needed by Jacobian operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.MutationNotSupported","page":"API reference","title":"DifferentiationInterface.MutationNotSupported","text":"MutationNotSupported\n\nTrait identifying backends that do not support two-argument functions f!(y, x).\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.MutationSupported","page":"API reference","title":"DifferentiationInterface.MutationSupported","text":"MutationSupported\n\nTrait identifying backends that support two-argument functions f!(y, x).\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PullbackExtras","page":"API reference","title":"DifferentiationInterface.PullbackExtras","text":"PullbackExtras\n\nAbstract type for additional information needed by pullback operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PullbackFast","page":"API reference","title":"DifferentiationInterface.PullbackFast","text":"PullbackFast\n\nTrait identifying backends that support efficient pullbacks.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PullbackSlow","page":"API reference","title":"DifferentiationInterface.PullbackSlow","text":"PullbackSlow\n\nTrait identifying backends that do not support efficient pullbacks.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PushforwardExtras","page":"API reference","title":"DifferentiationInterface.PushforwardExtras","text":"PushforwardExtras\n\nAbstract type for additional information needed by pushforward operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PushforwardFast","page":"API reference","title":"DifferentiationInterface.PushforwardFast","text":"PushforwardFast\n\nTrait identifying backends that support efficient pushforwards.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.PushforwardSlow","page":"API reference","title":"DifferentiationInterface.PushforwardSlow","text":"PushforwardSlow\n\nTrait identifying backends that do not support efficient pushforwards.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ReverseOverForward","page":"API reference","title":"DifferentiationInterface.ReverseOverForward","text":"ReverseOverForward\n\nTraits identifying second-order backends that compute HVPs in reverse over forward mode.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.ReverseOverReverse","page":"API reference","title":"DifferentiationInterface.ReverseOverReverse","text":"ReverseOverReverse\n\nTraits identifying second-order backends that compute HVPs in reverse over reverse mode.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.SecondDerivativeExtras","page":"API reference","title":"DifferentiationInterface.SecondDerivativeExtras","text":"SecondDerivativeExtras\n\nAbstract type for additional information needed by second derivative operators.\n\n\n\n\n\n","category":"type"},{"location":"api/#DifferentiationInterface.SymbolicsSparsityDetector","page":"API reference","title":"DifferentiationInterface.SymbolicsSparsityDetector","text":"SymbolicsSparsityDetector <: ADTypes.AbstractSparsityDetector\n\nSparsity detection algorithm based on the Symbolics.jl tracing system.\n\nCompatible with the ADTypes.jl sparsity detection framework.\n\ndanger: Danger\nThis functionality is implemented in an extension, and requires Symbolics.jl to be loaded.\n\nSee also\n\nADTypes.jacobian_sparsity\nADTypes.hessian_sparsity\n\nReference\n\nSparsity Programming: Automated Sparsity-Aware Optimizations in Differentiable Programming, Gowda et al. (2019)\n\n\n\n\n\n","category":"type"},{"location":"api/#ADTypes.mode-Tuple{SecondOrder}","page":"API reference","title":"ADTypes.mode","text":"mode(backend::SecondOrder)\n\nReturn the outer mode of the second-order backend.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.basis-Tuple{ADTypes.AbstractADType, AbstractArray, Any}","page":"API reference","title":"DifferentiationInterface.basis","text":"basis(backend, a::AbstractArray, i::CartesianIndex)\n\nConstruct the i-th stardard basis array in the vector space of a with element type eltype(a).\n\nNote\n\nIf an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.mutation_support-Tuple{ADTypes.AbstractADType}","page":"API reference","title":"DifferentiationInterface.mutation_support","text":"mutation_support(backend)\n\nReturn MutationSupported or MutationNotSupported in a statically predictable way.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.pick_chunksize-Tuple{Integer}","page":"API reference","title":"DifferentiationInterface.pick_chunksize","text":"pick_chunksize(input_length)\n\nPick a reasonable chunk size for chunked derivative evaluation with an input of length input_length.\n\nThe result cannot be larger than DEFAULT_CHUNKSIZE=8.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.pullback_performance-Tuple{ADTypes.AbstractADType}","page":"API reference","title":"DifferentiationInterface.pullback_performance","text":"pullback_performance(backend)\n\nReturn PullbackFast or PullbackSlow in a statically predictable way.\n\n\n\n\n\n","category":"method"},{"location":"api/#DifferentiationInterface.pushforward_performance-Tuple{ADTypes.AbstractADType}","page":"API reference","title":"DifferentiationInterface.pushforward_performance","text":"pushforward_performance(backend)\n\nReturn PushforwardFast or PushforwardSlow in a statically predictable way.\n\n\n\n\n\n","category":"method"},{"location":"api/","page":"API reference","title":"API reference","text":"","category":"page"},{"location":"design/#Package-design","page":"Package design","title":"Package design","text":"","category":"section"},{"location":"design/#ssec-requirements","page":"Package design","title":"Backend requirements","text":"","category":"section"},{"location":"design/","page":"Package design","title":"Package design","text":"To be usable with DifferentiationInterface.jl, an AD backend needs an object subtyping ADTypes.AbstractADType. In addition, some operators must be defined:","category":"page"},{"location":"design/","page":"Package design","title":"Package design","text":"backend subtype pushforward necessary pullback necessary\nADTypes.ForwardMode yes no\nADTypes.ReverseMode no yes\nADTypes.SymbolicMode yes yes","category":"page"},{"location":"design/","page":"Package design","title":"Package design","text":"Every backend we support corresponds to a package extension of DifferentiationInterface.jl (located in the ext subfolder). Advanced users are welcome to code more backends and submit pull requests!","category":"page"},{"location":"design/","page":"Package design","title":"Package design","text":"","category":"page"},{"location":"overloads/#Table-of-overloads","page":"Table of overloads","title":"Table of overloads","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"As described in the overview, DifferentiationInterface provides multiple high-level operators like jacobian, each with several variants: ","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"out-of-place or in-place return values\nwith or without primal output value\nsupport for one-argument functions y = f(x) or two-argument functions f!(y, x)","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"To support a new backend, it is only required to define either a pushforward or a pullback function, since DifferentiationInterface provides default implementations of all operators using just these two primitives. However, backends sometimes provide their own implementations of operators, which can be more performant. When available, DifferentiationInterface always calls these backend-specific implementations, which we call \"overloads\".","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"The following tables summarize all implemented overloads for each backend. Each cell can have three values:","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"❌: the operator is not overloaded because the backend does not support it\n✅: the operator is overloaded\nNA: the operator does not exist","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"tip: Tip\nCheck marks (✅) are clickable and link to the source code.","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"using ADTypes: AbstractADType\nusing DifferentiationInterface\nusing DifferentiationInterface: backend_str, mutation_support, MutationSupported\nusing Markdown: Markdown\nusing Diffractor: Diffractor\nusing Enzyme: Enzyme\nusing FastDifferentiation: FastDifferentiation\nusing FiniteDiff: FiniteDiff\nusing FiniteDifferences: FiniteDifferences\nusing ForwardDiff: ForwardDiff\nusing PolyesterForwardDiff: PolyesterForwardDiff\nusing ReverseDiff: ReverseDiff\nusing Tapir: Tapir\nusing Tracker: Tracker\nusing Zygote: Zygote\n\nfunction operators_and_types_f(backend::T) where {T<:AbstractADType}\n return (\n # (op, types_op), \n # (op!, types_op!), \n # (val_and_op, types_val_and_op),\n # (val_and_op!, types_val_and_op!),\n (\n (:derivative, (Any, T, Any, Any)),\n (:derivative!, (Any, Any, T, Any, Any)),\n (:value_and_derivative, (Any, T, Any, Any)),\n (:value_and_derivative!, (Any, Any, T, Any, Any)),\n ),\n (\n (:gradient, (Any, T, Any, Any)),\n (:gradient!, (Any, Any, T, Any, Any)),\n (:value_and_gradient, (Any, T, Any, Any)),\n (:value_and_gradient!, (Any, Any, T, Any, Any)),\n ),\n (\n (:jacobian, (Any, T, Any, Any)),\n (:jacobian!, (Any, Any, T, Any, Any)),\n (:value_and_jacobian, (Any, T, Any, Any)),\n (:value_and_jacobian!, (Any, Any, T, Any, Any)),\n ),\n (\n (:hessian, (Any, T, Any, Any)),\n (:hessian!, (Any, Any, T, Any, Any)),\n (nothing, nothing),\n (nothing, nothing),\n ),\n (\n (:hvp, (Any, T, Any, Any, Any)),\n (:hvp!, (Any, Any, T, Any, Any, Any)),\n (nothing, nothing),\n (nothing, nothing),\n ),\n (\n (:pullback, (Any, T, Any, Any, Any)),\n (:pullback!, (Any, Any, T, Any, Any, Any)),\n (:value_and_pullback, (Any, T, Any, Any, Any)),\n (:value_and_pullback!, (Any, Any, T, Any, Any, Any)),\n ),\n (\n (:pushforward, (Any, T, Any, Any, Any)),\n (:pushforward!, (Any, Any, T, Any, Any, Any)),\n (:value_and_pushforward, (Any, T, Any, Any, Any)),\n (:value_and_pushforward!, (Any, Any, T, Any, Any, Any)),\n ),\n )\nend\nfunction operators_and_types_f!(backend::T) where {T<:AbstractADType}\n return (\n (\n (:derivative, (Any, Any, T, Any, Any)),\n (:derivative!, (Any, Any, Any, T, Any, Any)),\n (:value_and_derivative, (Any, Any, T, Any, Any)),\n (:value_and_derivative!, (Any, Any, Any, T, Any, Any)),\n ),\n (\n (:jacobian, (Any, Any, T, Any, Any)),\n (:jacobian!, (Any, Any, Any, T, Any, Any)),\n (:value_and_jacobian, (Any, Any, T, Any, Any)),\n (:value_and_jacobian!, (Any, Any, Any, T, Any, Any)),\n ),\n (\n (:pullback, (Any, Any, T, Any, Any, Any)),\n (:pullback!, (Any, Any, Any, T, Any, Any, Any)),\n (:value_and_pullback, (Any, Any, T, Any, Any, Any)),\n (:value_and_pullback!, (Any, Any, Any, T, Any, Any, Any)),\n ),\n (\n (:pushforward, (Any, Any, T, Any, Any, Any)),\n (:pushforward!, (Any, Any, Any, T, Any, Any, Any)),\n (:value_and_pushforward, (Any, Any, T, Any, Any, Any)),\n (:value_and_pushforward!, (Any, Any, Any, T, Any, Any, Any)),\n ),\n )\nend\n\nfunction method_overloaded(operator::Symbol, argtypes, ext::Module)\n f = @eval DifferentiationInterface.$operator\n ms = methods(f, argtypes, ext)\n\n n = length(ms)\n n == 0 && return \"❌\"\n n == 1 && return \"[✅]($(Base.url(only(ms))))\"\n return \"[✅]($(Base.url(first(ms))))\" # Optional TODO: return all URLs?\nend\n\nfunction print_overload_table(io::IO, operators_and_types, ext::Module)\n println(io, \"| Operator | `op` | `op!` | `value_and_op` | `value_and_op!` |\")\n println(io, \"|:---------|:----:|:-----:|:--------------:|:---------------:|\")\n for operator_variants in operators_and_types\n opname = first(first(operator_variants))\n print(io, \"| `$opname` |\")\n for (op, type_signature) in operator_variants\n if isnothing(op)\n print(io, \"NA\")\n else\n print(io, method_overloaded(op, type_signature, ext))\n end\n print(io, '|')\n end\n println(io)\n end\nend\n\nfunction print_overloads(backend, ext::Symbol)\n io = IOBuffer()\n ext = Base.get_extension(DifferentiationInterface, ext)\n\n println(io, \"#### One-argument functions `y = f(x)`\")\n println(io)\n print_overload_table(io, operators_and_types_f(backend), ext)\n\n println(io, \"#### Two-argument functions `f!(y, x)`\")\n println(io)\n if mutation_support(backend) == MutationSupported()\n print_overload_table(io, operators_and_types_f!(backend), ext)\n else\n println(io, \"Backend doesn't support mutating functions.\")\n end\n\n return Markdown.parse(String(take!(io)))\nend","category":"page"},{"location":"overloads/#Diffractor-(forward/reverse)","page":"Table of overloads","title":"Diffractor (forward/reverse)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoDiffractor(), :DifferentiationInterfaceDiffractorExt) # hide","category":"page"},{"location":"overloads/#Enzyme-(forward)","page":"Table of overloads","title":"Enzyme (forward)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoEnzyme(; mode=Enzyme.Forward), :DifferentiationInterfaceEnzymeExt) # hide","category":"page"},{"location":"overloads/#Enzyme-(reverse)","page":"Table of overloads","title":"Enzyme (reverse)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoEnzyme(; mode=Enzyme.Reverse), :DifferentiationInterfaceEnzymeExt) # hide","category":"page"},{"location":"overloads/#FastDifferentiation-(symbolic)","page":"Table of overloads","title":"FastDifferentiation (symbolic)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoFastDifferentiation(), :DifferentiationInterfaceFastDifferentiationExt) # hide","category":"page"},{"location":"overloads/#FiniteDiff-(forward)","page":"Table of overloads","title":"FiniteDiff (forward)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoFiniteDiff(), :DifferentiationInterfaceFiniteDiffExt) # hide","category":"page"},{"location":"overloads/#FiniteDifferences-(forward)","page":"Table of overloads","title":"FiniteDifferences (forward)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoFiniteDifferences(; fdm=FiniteDifferences.central_fdm(3, 1)), :DifferentiationInterfaceFiniteDifferencesExt) # hide","category":"page"},{"location":"overloads/#ForwardDiff-(forward)","page":"Table of overloads","title":"ForwardDiff (forward)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoForwardDiff(), :DifferentiationInterfaceForwardDiffExt) # hide","category":"page"},{"location":"overloads/#PolyesterForwardDiff-(forward)","page":"Table of overloads","title":"PolyesterForwardDiff (forward)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoPolyesterForwardDiff(; chunksize=1), :DifferentiationInterfacePolyesterForwardDiffExt) # hide","category":"page"},{"location":"overloads/#ReverseDiff-(reverse)","page":"Table of overloads","title":"ReverseDiff (reverse)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoReverseDiff(), :DifferentiationInterfaceReverseDiffExt) # hide","category":"page"},{"location":"overloads/#Tapir-(reverse)","page":"Table of overloads","title":"Tapir (reverse)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoTapir(), :DifferentiationInterfaceTapirExt) # hide","category":"page"},{"location":"overloads/#Tracker-(reverse)","page":"Table of overloads","title":"Tracker (reverse)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoTracker(), :DifferentiationInterfaceTrackerExt) # hide","category":"page"},{"location":"overloads/#Zygote-(reverse)","page":"Table of overloads","title":"Zygote (reverse)","text":"","category":"section"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"print_overloads(AutoZygote(), :DifferentiationInterfaceZygoteExt) # hide","category":"page"},{"location":"overloads/","page":"Table of overloads","title":"Table of overloads","text":"","category":"page"},{"location":"overview/#sec-overview","page":"Overview","title":"Overview","text":"","category":"section"},{"location":"overview/#Operators","page":"Overview","title":"Operators","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"Depending on the type of input and output, differentiation operators can have various names.","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"We provide the following high-level operators:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"operator order input x output y result type result shape\nderivative 1 Number Number or AbstractArray same as y size(y)\nsecond_derivative 2 Number Number or AbstractArray same as y size(y)\ngradient 1 AbstractArray Number same as x size(x)\nhvp 2 AbstractArray Number same as x size(x)\nhessian 2 AbstractArray Number AbstractMatrix (length(x), length(x))\njacobian 1 AbstractArray AbstractArray AbstractMatrix (length(y), length(x))","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"They can all be derived from two low-level operators:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"operator order input x output y result type result shape\npushforward (or JVP) 1 Any Any same as y size(y)\npullback (or VJP) 1 Any Any same as x size(x)","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"Luckily, most backends have custom implementations, which we reuse if possible instead of relying on fallbacks.","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"tip: Tip\nSee the book The Elements of Differentiable Programming for details on these concepts.","category":"page"},{"location":"overview/#Variants","page":"Overview","title":"Variants","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"Several variants of each operator are defined:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"out-of-place in-place out-of-place + primal in-place + primal\nderivative derivative! value_and_derivative value_and_derivative!\nsecond_derivative second_derivative! NA NA\ngradient gradient! value_and_gradient value_and_gradient!\nhvp hvp! NA NA\nhessian hessian! NA NA\njacobian jacobian! value_and_jacobian value_and_jacobian!\npushforward pushforward! value_and_pushforward value_and_pushforward!\npullback pullback! value_and_pullback value_and_pullback!","category":"page"},{"location":"overview/#Mutation-and-signatures","page":"Overview","title":"Mutation and signatures","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"In order to ensure symmetry between one-argument functions f(x) = y and two-argument functions f!(y, x) = nothing, we define the same operators for both cases. However they have different signatures:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"signature out-of-place in-place\nf(x) operator(f, backend, x, ...) operator!(f, result, backend, x, ...)\nf!(y, x) operator(f!, y, backend, x, ...) operator!(f!, y, result, backend, x, ...)","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"warning: Warning\nOur mutation convention is that all positional arguments between f/f! and backend are mutated (the extras as well, see below). This convention holds regardless of the bang ! in the operator name, because we assume that a user passing a two-argument function f!(y, x) anticipates mutation anyway.Still, better be careful with two-argument functions, because every variant of the operator will mutate y... even if it does not have a ! in its name (see the bottom left cell in the table).","category":"page"},{"location":"overview/#Preparation","page":"Overview","title":"Preparation","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"In many cases, AD can be accelerated if the function has been run at least once (e.g. to create a config or record a tape) and if some cache objects are provided. This is a backend-specific procedure, but we expose a common syntax to achieve it.","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"operator preparation function\nderivative prepare_derivative\ngradient prepare_gradient\njacobian prepare_jacobian\nsecond_derivative prepare_second_derivative\nhessian prepare_hessian\npushforward prepare_pushforward\npullback prepare_pullback\nhvp prepare_hvp","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"Unsurprisingly, preparation syntax depends on the number of arguments:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"signature preparation signature\nf(x) prepare_operator(f, backend, x, ...)\nf!(y, x) prepare_operator(f!, y, backend, x, ...)","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"The preparation prepare_operator(f, backend, x) will create an object called extras containing the necessary information to speed up operator and its variants. This information is specific to backend and f, as well as the type and size of the input x and the control flow within the function, but it should work with different values of x.","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"You can then call e.g. operator(backend, f, x2, extras), which should be faster than operator(f, backend, x2). This is especially worth it if you plan to call operator several times in similar settings: you can think of it as a warm up.","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"warning: Warning\nThe extras object is nearly always mutated when given to an operator, even when said operator does not have a bang ! in its name.","category":"page"},{"location":"overview/#Second-order","page":"Overview","title":"Second order","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"We offer two ways to perform second-order differentiation (for second_derivative, hvp and hessian):","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"pick a single backend to do all the work\ncombine an \"outer\" and \"inner\" backend within the SecondOrder struct: the inner backend will be called first, and the outer backend will differentiate the generated code","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"warning: Warning\nThere are many possible backend combinations, a lot of which will fail. At the moment, trial and error is your best friend. Usually, the most efficient approach for Hessians is forward-over-reverse, i.e. a forward-mode outer backend and a reverse-mode inner backend.","category":"page"},{"location":"overview/#Experimental","page":"Overview","title":"Experimental","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"danger: Danger\nEverything in this section is still experimental, use it at your own risk.","category":"page"},{"location":"overview/#Sparsity","page":"Overview","title":"Sparsity","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"ADTypes.jl provides AutoSparse to accelerate the computation of sparse Jacobians and Hessians:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"for sparse Jacobians, wrap AutoSparse around a first-order backend.\nfor sparse Hessians, wrap AutoSparse around a SecondOrder backend.","category":"page"},{"location":"overview/#Split-reverse-mode","page":"Overview","title":"Split reverse mode","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"Some reverse mode AD backends expose a \"split\" option, which runs only the forward sweep, and encapsulates the reverse sweep in a closure. We make this available for all backends with the following operators:","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"out-of-place in-place\nvalue_and_pullback_split value_and_pullback!_split","category":"page"},{"location":"overview/#Translation","page":"Overview","title":"Translation","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"The wrapper DifferentiateWith allows you to take a function and specify that it should be differentiated with the backend of your choice. In other words, when you try to differentiate dw = DifferentiateWith(f, backend1) with backend2, then backend1 steps in and backend2 does nothing. At the moment it only works when backend2 supports ChainRules.jl.","category":"page"},{"location":"overview/#Going-further","page":"Overview","title":"Going further","text":"","category":"section"},{"location":"overview/#Non-standard-types","page":"Overview","title":"Non-standard types","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"The package is thoroughly tested with inputs and outputs of the following types: Float64, Vector{Float64} and Matrix{Float64}. We also expect it to work on most kinds of Number and AbstractArray variables. Beyond that, you are in uncharted territory. We voluntarily keep the type annotations minimal, so that passing more complex objects or custom structs might work with some backends, but we make no guarantees about that.","category":"page"},{"location":"overview/#Multiple-inputs/outputs","page":"Overview","title":"Multiple inputs/outputs","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"Restricting the API to one input and one output has many coding advantages, but it is not very flexible. If you need more than that, use ComponentArrays.jl to wrap several objects inside a single ComponentVector.","category":"page"},{"location":"overview/#Batched-evaluation","page":"Overview","title":"Batched evaluation","text":"","category":"section"},{"location":"overview/","page":"Overview","title":"Overview","text":"This is not supported at the moment, but we plan to allow several pushforward / pullback seeds at once (similar to the chunking in ForwardDiff.jl or the batches in Enzyme.jl).","category":"page"},{"location":"overview/","page":"Overview","title":"Overview","text":"","category":"page"},{"location":"backends/","page":"Backends","title":"Backends","text":"CurrentModule = Main\nCollapsedDocStrings = true","category":"page"},{"location":"backends/","page":"Backends","title":"Backends","text":"using DifferentiationInterface\nusing DifferentiationInterface: backend_str\nimport Markdown\nimport Diffractor, Enzyme, FastDifferentiation, FiniteDiff, FiniteDifferences, ForwardDiff, PolyesterForwardDiff, ReverseDiff, Tapir, Tracker, Zygote\n\nconst backend_examples = (\n \"AutoDiffractor()\",\n \"AutoEnzyme(; mode=Enzyme.Forward)\",\n \"AutoEnzyme(; mode=Enzyme.Reverse)\",\n \"AutoFastDifferentiation()\",\n \"AutoFiniteDiff()\",\n \"AutoFiniteDifferences(; fdm=FiniteDifferences.central_fdm(3, 1))\",\n \"AutoForwardDiff()\",\n \"AutoPolyesterForwardDiff(; chunksize=1)\",\n \"AutoReverseDiff()\",\n \"AutoTapir()\",\n \"AutoTracker()\",\n \"AutoZygote()\",\n)\n\ncheckmark(x::Bool) = x ? '✅' : '❌'\nunicode_check_available(backend) = checkmark(check_available(backend))\nunicode_check_hessian(backend) = checkmark(check_hessian(backend))\nunicode_check_twoarg(backend) = checkmark(check_twoarg(backend))\n\nio = IOBuffer()\n\n# Table header \nprintln(io, \"| Backend | Availability | Two-argument functions | Hessian support | Example |\")\nprintln(io, \"|:--------|:------------:|:----------------------:|:---------------:|:--------|\")\n\nfor example in backend_examples\n b = eval(Meta.parse(example)) # backend\n join(io, [backend_str(b), unicode_check_available(b), unicode_check_twoarg(b), unicode_check_hessian(b), \"`$example`\"], '|')\n println(io, '|' )\nend\nbackend_table = Markdown.parse(String(take!(io)))","category":"page"},{"location":"backends/#Backends","page":"Backends","title":"Backends","text":"","category":"section"},{"location":"backends/#Types","page":"Backends","title":"Types","text":"","category":"section"},{"location":"backends/","page":"Backends","title":"Backends","text":"We support all dense backend choices from ADTypes.jl, as well as their sparse wrapper AutoSparse.","category":"page"},{"location":"backends/","page":"Backends","title":"Backends","text":"For sparse backends, only the Jacobian and Hessian operators are implemented differently, the other operators behave the same as for the corresponding dense backend.","category":"page"},{"location":"backends/","page":"Backends","title":"Backends","text":"backend_table #hide","category":"page"},{"location":"backends/#Availability","page":"Backends","title":"Availability","text":"","category":"section"},{"location":"backends/","page":"Backends","title":"Backends","text":"You can use check_available to verify whether a given backend is loaded.","category":"page"},{"location":"backends/#Support-for-two-argument-functions","page":"Backends","title":"Support for two-argument functions","text":"","category":"section"},{"location":"backends/","page":"Backends","title":"Backends","text":"All backends are compatible with one-argument functions f(x) = y. Only some are compatible with two-argument functions f!(y, x) = nothing. You can check this compatibility using check_twoarg.","category":"page"},{"location":"backends/#Hessian-support","page":"Backends","title":"Hessian support","text":"","category":"section"},{"location":"backends/","page":"Backends","title":"Backends","text":"Only some backends are able to compute Hessians. You can use check_hessian to check this feature.","category":"page"},{"location":"backends/#API-reference","page":"Backends","title":"API reference","text":"","category":"section"},{"location":"backends/","page":"Backends","title":"Backends","text":"warning: Warning\nThe following documentation has been re-exported from ADTypes.jl. Refer to the ADTypes documentation for more information.","category":"page"},{"location":"backends/","page":"Backends","title":"Backends","text":"ADTypes\nADTypes.AbstractADType\nAutoChainRules\nAutoDiffractor\nAutoEnzyme\nAutoFastDifferentiation\nAutoFiniteDiff\nAutoFiniteDifferences\nAutoForwardDiff\nAutoPolyesterForwardDiff\nAutoReverseDiff\nAutoSymbolics\nAutoTapir\nAutoTracker\nAutoZygote\nAutoSparse","category":"page"},{"location":"backends/#ADTypes.ADTypes","page":"Backends","title":"ADTypes.ADTypes","text":"ADTypes.jl\n\nADTypes.jl is a multi-valued logic system to choose an automatic differentiation (AD) package and specify its parameters.\n\n\n\n\n\n","category":"module"},{"location":"backends/#ADTypes.AbstractADType","page":"Backends","title":"ADTypes.AbstractADType","text":"AbstractADType\n\nAbstract supertype for all AD choices.\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoChainRules","page":"Backends","title":"ADTypes.AutoChainRules","text":"AutoChainRules{RC}\n\nChooses any AD library based on ChainRulesCore.jl (see the list here).\n\nFields\n\nruleconfig::RC: a ChainRulesCore.RuleConfig object.\n\nConstructor\n\nAutoChainRules(; ruleconfig)\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoDiffractor","page":"Backends","title":"ADTypes.AutoDiffractor","text":"AutoDiffractor\n\nChooses Diffractor.jl.\n\nConstructor\n\nAutoDiffractor()\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoEnzyme","page":"Backends","title":"ADTypes.AutoEnzyme","text":"AutoEnzyme{M}\n\nChooses Enzyme.jl.\n\nFields\n\nmode::M: can be either \nan object subtyping EnzymeCore.Mode (like EnzymeCore.Forward or EnzymeCore.Reverse) if a specific mode is required\nnothing to choose the best mode automatically\n\nConstructors\n\nAutoEnzyme(; mode=nothing)\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoFastDifferentiation","page":"Backends","title":"ADTypes.AutoFastDifferentiation","text":"AutoFastDifferentiation\n\nChooses FastDifferentiation.jl.\n\nConstructor\n\nAutoFastDifferentiation()\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoFiniteDiff","page":"Backends","title":"ADTypes.AutoFiniteDiff","text":"AutoFiniteDiff{T1,T2,T3}\n\nChooses FiniteDiff.jl.\n\nFields\n\nfdtype::T1: finite difference type\nfdjtype::T2: finite difference type for the Jacobian\nfdhtype::T3: finite difference type for the Hessian\n\nConstructor\n\nAutoFiniteDiff(; fdtype=Val(:forward), fdjtype=fdtype, fdhtype=Val(:hcentral))\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoFiniteDifferences","page":"Backends","title":"ADTypes.AutoFiniteDifferences","text":"AutoFiniteDifferences{T}\n\nChooses FiniteDifferences.jl.\n\nFields\n\nfdm::T: a FiniteDifferenceMethod\n\nConstructor\n\nAutoFiniteDifferences(; fdm)\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoForwardDiff","page":"Backends","title":"ADTypes.AutoForwardDiff","text":"AutoForwardDiff{chunksize,T}\n\nChooses ForwardDiff.jl.\n\nType parameters\n\nchunksize: the preferred chunk size to evaluate several derivatives at once\n\nFields\n\ntag::T: a custom tag to handle nested differentiation calls (usually not necessary)\n\nConstructors\n\nAutoForwardDiff(; chunksize=nothing, tag=nothing)\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoPolyesterForwardDiff","page":"Backends","title":"ADTypes.AutoPolyesterForwardDiff","text":"AutoPolyesterForwardDiff{chunksize,T}\n\nChooses PolyesterForwardDiff.jl.\n\nType parameters\n\nchunksize: the preferred chunk size to evaluate several derivatives at once\n\nFields\n\ntag::T: a custom tag to handle nested differentiation calls (usually not necessary)\n\nConstructors\n\nAutoPolyesterForwardDiff(; chunksize=nothing, tag=nothing)\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoReverseDiff","page":"Backends","title":"ADTypes.AutoReverseDiff","text":"AutoReverseDiff\n\nChooses ReverseDiff.jl.\n\nFields\n\ncompile::Bool: whether to compile the tape prior to differentiation\n\nConstructor\n\nAutoReverseDiff(; compile=false)\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoSymbolics","page":"Backends","title":"ADTypes.AutoSymbolics","text":"AutoSymbolics\n\nChooses Symbolics.jl.\n\nConstructor\n\nAutoSymbolics()\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoTapir","page":"Backends","title":"ADTypes.AutoTapir","text":"AutoTapir\n\nChooses Tapir.jl.\n\nConstructor\n\nAutoTapir()\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoTracker","page":"Backends","title":"ADTypes.AutoTracker","text":"AutoTracker\n\nChooses Tracker.jl.\n\nConstructor\n\nAutoTracker()\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoZygote","page":"Backends","title":"ADTypes.AutoZygote","text":"AutoZygote\n\nChooses Zygote.jl.\n\nConstructor\n\nAutoZygote()\n\n\n\n\n\n","category":"type"},{"location":"backends/#ADTypes.AutoSparse","page":"Backends","title":"ADTypes.AutoSparse","text":"AutoSparse{D,S,C}\n\nWraps an ADTypes.jl object to deal with sparse Jacobians and Hessians.\n\nFields\n\ndense_ad::D: the underlying AD package, subtyping AbstractADType\nsparsity_detector::S: the sparsity pattern detector, subtyping AbstractSparsityDetector\ncoloring_algorithm::C: the coloring algorithm, subtyping AbstractColoringAlgorithm\n\nConstructors\n\nAutoSparse(\n dense_ad;\n sparsity_detector=ADTypes.NoSparsityDetector(),\n coloring_algorithm=ADTypes.NoColoringAlgorithm()\n)\n\n\n\n\n\n","category":"type"},{"location":"backends/","page":"Backends","title":"Backends","text":"","category":"page"},{"location":"#DifferentiationInterface","page":"Home","title":"DifferentiationInterface","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"(Image: Build Status) (Image: Coverage) (Image: Code Style: Blue)","category":"page"},{"location":"","page":"Home","title":"Home","text":"Package Docs\nDifferentiationInterface (Image: Stable) (Image: Dev)\nDifferentiationInterfaceTest (Image: Stable) (Image: Dev)","category":"page"},{"location":"","page":"Home","title":"Home","text":"An interface to various automatic differentiation (AD) backends in Julia.","category":"page"},{"location":"#Goal","page":"Home","title":"Goal","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"This package provides a backend-agnostic syntax to differentiate functions of the following types:","category":"page"},{"location":"","page":"Home","title":"Home","text":"one-argument functions (allocating): f(x) = y\ntwo-argument functions (mutating): f!(y, x) = nothing","category":"page"},{"location":"#Features","page":"Home","title":"Features","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"First- and second-order operators\nIn-place and out-of-place differentiation\nPreparation mechanism (e.g. to create a config or tape)\nThorough validation on standard inputs and outputs (numbers, vectors, matrices)\nTesting and benchmarking utilities accessible to users with DifferentiationInterfaceTest","category":"page"},{"location":"#Compatibility","page":"Home","title":"Compatibility","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"We support all of the backends defined by ADTypes.jl v1.0:","category":"page"},{"location":"","page":"Home","title":"Home","text":"ChainRulesCore.jl\nDiffractor.jl\nEnzyme.jl\nFastDifferentiation.jl\nFiniteDiff.jl\nFiniteDifferences.jl\nForwardDiff.jl\nPolyesterForwardDiff.jl\nReverseDiff.jl\nSparseDiffTools.jl\nSymbolics.jl\nTapir.jl\nTracker.jl\nZygote.jl","category":"page"},{"location":"#Installation","page":"Home","title":"Installation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"To install the stable version of the package, run the following code in a Julia REPL:","category":"page"},{"location":"","page":"Home","title":"Home","text":"julia> using Pkg\n\njulia> Pkg.add(\"DifferentiationInterface\")","category":"page"},{"location":"","page":"Home","title":"Home","text":"To install the development version, run this instead:","category":"page"},{"location":"","page":"Home","title":"Home","text":"julia> using Pkg\n\njulia> Pkg.add(\n url=\"https://github.com/gdalle/DifferentiationInterface.jl\",\n subdir=\"DifferentiationInterface\"\n )","category":"page"},{"location":"#Example","page":"Home","title":"Example","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"julia> import ADTypes, ForwardDiff\n\njulia> using DifferentiationInterface\n\njulia> backend = ADTypes.AutoForwardDiff();\n\njulia> f(x) = sum(abs2, x);\n\njulia> value_and_gradient(f, backend, [1., 2., 3.])\n(14.0, [2.0, 4.0, 6.0])","category":"page"},{"location":"#Related-packages","page":"Home","title":"Related packages","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"AbstractDifferentiation.jl is the original inspiration for DifferentiationInterface.jl.\nAutoDiffOperators.jl is an attempt to bridge ADTypes.jl with AbstractDifferentiation.jl.","category":"page"},{"location":"","page":"Home","title":"Home","text":"","category":"page"},{"location":"extensions/#Package-extensions","page":"Package extensions","title":"Package extensions","text":"","category":"section"},{"location":"extensions/","page":"Package extensions","title":"Package extensions","text":"CurrentModule = DifferentiationInterface","category":"page"},{"location":"extensions/","page":"Package extensions","title":"Package extensions","text":"Package extension content is not part of the public API. If any docstrings are present in an extension, they will appear below.","category":"page"},{"location":"extensions/","page":"Package extensions","title":"Package extensions","text":"Modules = [\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceChainRulesCoreExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceDiffractorExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceEnzymeExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceFastDifferentiationExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceFiniteDiffExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceFiniteDifferencesExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceForwardDiffExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfacePolyesterForwardDiffExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceReverseDiffExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceSymbolicsExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceTapirExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceTrackerExt),\n Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceZygoteExt)\n]\nFilter = t -> !(t isa Type && t <: ADTypes.AbstractADType)","category":"page"},{"location":"extensions/","page":"Package extensions","title":"Package extensions","text":"","category":"page"}] +} diff --git a/DifferentiationInterface/previews/PR220/siteinfo.js b/DifferentiationInterface/previews/PR220/siteinfo.js new file mode 100644 index 000000000..febd11bca --- /dev/null +++ b/DifferentiationInterface/previews/PR220/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR220"; diff --git a/DifferentiationInterface/previews/PR220/tutorial/index.html b/DifferentiationInterface/previews/PR220/tutorial/index.html new file mode 100644 index 000000000..420e0603b --- /dev/null +++ b/DifferentiationInterface/previews/PR220/tutorial/index.html @@ -0,0 +1,28 @@ + +Tutorial · DifferentiationInterface.jl
GitHub

Tutorial

We present a typical workflow with DifferentiationInterface.jl and showcase its potential performance benefits.

julia> using DifferentiationInterface
julia> import ADTypes, ForwardDiff, Enzyme
julia> using BenchmarkTools

Computing a gradient

A common use case of AD is optimizing real-valued functions with first- or second-order methods. Let's define a simple objective

julia> f(x::AbstractArray) = sum(abs2, x)f (generic function with 1 method)

and a random input vector

julia> x = [1.0, 2.0, 3.0];

To compute its gradient, we need to choose a "backend", i.e. an AD package that DifferentiationInterface.jl will call under the hood. Most backend types are defined by ADTypes.jl and re-exported by DifferentiationInterface.jl. ForwardDiff.jl is very generic and efficient for low-dimensional inputs, so it's a good starting point:

julia> backend = ADTypes.AutoForwardDiff()AutoForwardDiff{nothing, Nothing}(nothing)

Now you can use DifferentiationInterface.jl to get the gradient:

julia> gradient(f, backend, x)3-element Vector{Float64}:
+ 2.0
+ 4.0
+ 6.0

Was that fast? BenchmarkTools.jl helps you answer that question.

julia> @btime gradient($f, $backend, $x);  722.250 ns (5 allocations: 528 bytes)

More or less what you would get if you just used the API from ForwardDiff.jl:

julia> @btime ForwardDiff.gradient($f, $x);  694.837 ns (4 allocations: 432 bytes)

Not bad, but you can do better.

Overwriting a gradient

Since you know how much space your gradient will occupy, you can pre-allocate that memory and offer it to AD. Some backends get a speed boost from this trick.

julia> grad = zero(x)3-element Vector{Float64}:
+ 0.0
+ 0.0
+ 0.0
julia> gradient!(f, grad, backend, x);
julia> grad3-element Vector{Float64}:
+ 2.0
+ 4.0
+ 6.0

The bang indicates that one of the arguments of gradient! might be mutated. More precisely, our convention is that every positional argument between the function and the backend is mutated (and the extras too, see below).

julia> @btime gradient!($f, _grad, $backend, $x) evals=1 setup=(_grad=similar($x));  630.000 ns (4 allocations: 448 bytes)

For some reason the in-place version is not much better than your first attempt. However, it has one less allocation, which corresponds to the gradient vector you provided. Don't worry, you're not done yet.

Preparing for multiple gradients

Internally, ForwardDiff.jl creates some data structures to keep track of things. These objects can be reused between gradient computations, even on different input values. We abstract away the preparation step behind a backend-agnostic syntax:

julia> extras = prepare_gradient(f, backend, x)DifferentiationInterfaceForwardDiffExt.ForwardDiffGradientExtras{ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 3, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 3}}}}(ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 3, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 3}}}((Partials(1.0, 0.0, 0.0), Partials(0.0, 1.0, 0.0), Partials(0.0, 0.0, 1.0)), ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.f), Float64}, Float64, 3}[Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(1.0,1.0,0.0,0.0), Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(2.0,0.0,1.0,0.0), Dual{ForwardDiff.Tag{typeof(Main.f), Float64}}(3.0,0.0,0.0,1.0)]))

You don't need to know what this object is, you just need to pass it to the gradient operator.

julia> grad = zero(x);
julia> gradient!(f, grad, backend, x, extras);
julia> grad3-element Vector{Float64}:
+ 2.0
+ 4.0
+ 6.0

Preparation makes the gradient computation much faster, and (in this case) allocation-free.

julia> @btime gradient!($f, _grad, $backend, $x, _extras) evals=1 setup=(
+           _grad=similar($x);
+           _extras=prepare_gradient($f, $backend, $x)
+       );  60.000 ns (0 allocations: 0 bytes)

Beware that the extras object is nearly always mutated by differentiation operators, even though it is given as the last positional argument.

Switching backends

The whole point of DifferentiationInterface.jl is that you can easily experiment with different AD solutions. Typically, for gradients, reverse mode AD might be a better fit. So let's try the state-of-the-art Enzyme.jl!

For this one, the backend definition is slightly more involved, because you need to feed the "mode" to the object from ADTypes.jl:

julia> backend2 = ADTypes.AutoEnzyme(; mode=Enzyme.Reverse)AutoEnzyme{EnzymeCore.ReverseMode{false, EnzymeCore.FFIABI, false}}(EnzymeCore.ReverseMode{false, EnzymeCore.FFIABI, false}())

But once it is done, things run smoothly with exactly the same syntax:

julia> gradient(f, backend2, x)3-element Vector{Float64}:
+ 2.0
+ 4.0
+ 6.0

And you can run the same benchmarks:

julia> @btime gradient!($f, _grad, $backend2, $x, _extras) evals=1 setup=(
+           _grad=similar($x);
+           _extras=prepare_gradient($f, $backend2, $x)
+       );  3.536 μs (28 allocations: 1.55 KiB)

Not only is it blazingly fast, you achieved this speedup without looking at the docs of either ForwardDiff.jl or Enzyme.jl! In short, DifferentiationInterface.jl allows for easy testing and comparison of AD backends. If you want to go further, check out the DifferentiationTest.jl tutorial.